Error-correcting Identifying Codes
Discrete Mathematics
2022-04-26 v1 Combinatorics
Abstract
Assume that a graph models a detection system for a facility with a possible "intruder," or a multiprocessor network with a possible malfunctioning processor. We consider the problem of placing (the minimum number of) detectors at a subset of vertices in to automatically determine if there is an intruder, and if so, its precise location. In this research we explore a fault-tolerant variant of identifying codes, known as error-correcting identifying codes, which permit one false positive or negative and are applicable to real-world systems. We present the proof of NP-completeness of the problem of determining said minimum size in arbitrary graphs, and determine bounds on the parameter in cubic graphs.
Keywords
Cite
@article{arxiv.2204.11362,
title = {Error-correcting Identifying Codes},
author = {Devin Jean and Suk Seo},
journal= {arXiv preprint arXiv:2204.11362},
year = {2022}
}